Let m, n be fixed positive integers.
Prove that there are infinitely many triples of positive integers (x, y, z) such that
xmn+1 = ym + zn
for each pair of values (m, n).
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This course encompasses a range of Geometry topics such as coordinate and spatial geometry, introductory trigonometry, angles, parallel lines, congruent and similar triangles, polygons, circles, the Pythagorean Theorem, and more. Emphasis will be placed on reinforcing Algebra skills and enhancing critical thinking through problem-solving in both mathematical and real-world contexts.
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